61 ideas
| 125 | Is a gifted philosopher unmanly if he avoids the strife of the communal world? [Plato] |
| 6806 | Do not multiply entities beyond necessity [William of Ockham] |
| 1654 | In "Gorgias" Socrates is confident that his 'elenchus' will decide moral truth [Vlastos on Plato] |
| 4321 | We should test one another, by asking and answering questions [Plato] |
| 9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
| 9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
| 9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
| 9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
| 9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
| 9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
| 9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
| 9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
| 9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
| 9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
| 9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
| 9701 | A 'relation' is a set of ordered pairs [Enderton] |
| 9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
| 9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
| 9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
| 9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
| 9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
| 9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
| 9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
| 9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
| 9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
| 9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
| 9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
| 9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
| 9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
| 9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
| 9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
| 9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
| 9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
| 22132 | Species and genera are individual concepts which naturally signify many individuals [William of Ockham] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 114 | Rhetoric can produce conviction, but not educate people about right and wrong [Plato] |
| 116 | Rhetoric is irrational about its means and its ends [Plato] |
| 135 | All activity aims at the good [Plato] |
| 122 | Moral rules are made by the weak members of humanity [Plato] |
| 139 | A good person is bound to act well, and this brings happiness [Plato] |
| 128 | Is it natural to simply indulge our selfish desires? [Plato] |
| 4322 | In slaking our thirst the goodness of the action and the pleasure are clearly separate [Plato] |
| 136 | Good should be the aim of pleasant activity, not the other way round [Plato] |
| 134 | Good and bad people seem to experience equal amounts of pleasure and pain [Plato] |
| 132 | If happiness is the satisfaction of desires, then a life of scratching itches should be happiness [Plato] |
| 4319 | In a fool's mind desire is like a leaky jar, insatiable in its desires, and order and contentment are better [Plato] |
| 130 | Is the happiest state one of sensual, self-indulgent freedom? [Plato] |
| 120 | Should we avoid evil because it will bring us bad consequences? [Plato] |
| 118 | I would rather be a victim of crime than a criminal [Plato] |
| 131 | If absence of desire is happiness, then nothing is happier than a stone or a corpse [Plato] |
| 140 | Self-indulgent desire makes friendship impossible, because it makes a person incapable of co-operation [Plato] |
| 119 | A criminal is worse off if he avoids punishment [Plato] |
| 129 | Do most people praise self-discipline and justice because they are too timid to gain their own pleasure? [Plato] |
| 4320 | The popular view is that health is first, good looks second, and honest wealth third [Plato] |
| 137 | As with other things, a good state is organised and orderly [Plato] |
| 141 | A good citizen won't be passive, but will redirect the needs of the state [Plato] |
| 123 | Do most people like equality because they are second-rate? [Plato] |
| 124 | Does nature imply that it is right for better people to have greater benefits? [Plato] |
| 19381 | The past has ceased to exist, and the future does not yet exist, so time does not exist [William of Ockham] |
| 8010 | William of Ockham is the main spokesman for God's commands being the source of morality [William of Ockham] |
| 16679 | Even an angel must have some location [William of Ockham, by Pasnau] |